# Question

Dr. Harold Wolf of Medical Research Corporation (MRC) was thrilled with the response he had received from drug companies for his latest discovery, a unique electronic stimulator that reduces the pain from arthritis. The process had yet to pass rigorous Federal Drug Administration (FDA) testing and was still in the early stages of development, but the interest was intense. He received the three offers described following this paragraph. (A 10 percent interest rate should be used throughout this analysis unless otherwise specified.)

Offer I - $1,000,000 now plus $200,000 from year 6 through 15. Also, if the product did over $100 million in cumulative sales by the end of year 15, he would receive an additional $3,000,000. Dr. Wolf thought there was a 70 percent probability this would happen.

Offer II - Thirty percent of the buyer’s gross profit on the product for the next four years. The buyer in this case was Zbay Pharmaceutical. Zbay’s gross profit margin was 60 percent. Sales in year one were projected to be $2 million and then expected to grow by 40 percent per year.

Offer III - A trust fund would be set up for the next eight years. At the end of that period, Dr. Wolf would receive the proceeds (and discount them back to the present at 10 percent). The trust fund called for semiannual payments for the next eight years of $200,000 (a total of $400,000 per year).

The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. To look up the future value of an annuity due in the tables, add 1 to n (16 + 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 10 percent annually (5 percent semiannually). Determine the present value of the trust fund’s final value.

Required:

Find the present value of each of the three offers and indicate which one has the highest present value.

Offer I - $1,000,000 now plus $200,000 from year 6 through 15. Also, if the product did over $100 million in cumulative sales by the end of year 15, he would receive an additional $3,000,000. Dr. Wolf thought there was a 70 percent probability this would happen.

Offer II - Thirty percent of the buyer’s gross profit on the product for the next four years. The buyer in this case was Zbay Pharmaceutical. Zbay’s gross profit margin was 60 percent. Sales in year one were projected to be $2 million and then expected to grow by 40 percent per year.

Offer III - A trust fund would be set up for the next eight years. At the end of that period, Dr. Wolf would receive the proceeds (and discount them back to the present at 10 percent). The trust fund called for semiannual payments for the next eight years of $200,000 (a total of $400,000 per year).

The payments would start immediately. Since the payments are coming at the beginning of each period instead of the end, this is an annuity due. To look up the future value of an annuity due in the tables, add 1 to n (16 + 1) and subtract 1 from the value in the table. Assume the annual interest rate on this annuity is 10 percent annually (5 percent semiannually). Determine the present value of the trust fund’s final value.

Required:

Find the present value of each of the three offers and indicate which one has the highest present value.

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